Magnetic Anisotropy Field Research Articles

Exploring stress-dependent impedance behavior via magnetization dynamics in amorphous magnetic fibers in high frequency: Experimental and modeling

The magnetoelastic effect plays a crucial role in influencing the magnetization dynamics and impedance characteristics of magnetic fibers (MFs). In this work, we investigate the modulation of the domain structure and impedance behaviors under stress within Co-based MFs aided by experimental and theoretical approaches. The remarkable changes of natural ferromagnetic resonance and the transition of domain inclination angles indicate that the stress-impedance effect derives from the evolution of the magnetic domain structure and anisotropy field, which are induced by magnetoelastic coupling. The ferromagnetic resonance linewidths over a range of applied tensile strains (0–0.54%) serve to elucidate the contribution of magnetoelastic coupling to magnetic damping in ferromagnetic fibers. By utilizing the shell domain expansion method, we derive circular dynamic permeability and compute the impedance properties at high frequencies of MFs under multi-field stimulus. The theoretical model accurately predicts key features of magnetization dynamics, the evolution of ferromagnetic resonance, and impedance curves of MFs, in good agreement with experimental results including very fine observation of domain evolution. This comprehensive approach provides profound insights into the stress modulation of impedance characteristics, with implications for sensing applications of MFs.

Enhanced Electromagnetic Wave Absorption in W-Type Ba-Hexaferrites: Role of Composition and Grain Growth

W-type Ba-hexaferrite, BaZn2−xCoxFe16O27, was synthesized via both conventional solid-state (x = 0.4, 0.5, 0.6, 0.75, 1.0, 1.25, 1.5) and molten-salt methods (x = 0.75, 1.0, 1.25). The structure, electromagnetic (EM) properties, and EM wave absorption characteristics were examined across a frequency range of 0.1–18 GHz, focusing on the influence of varying x. As x increased from 0.4 to 0.75, the magnetic anisotropy field (Hani) decreased, reaching its minimum at x = 0.75, before rising again as x continued to increase up to 1.5. Hani was found to be proportional to the ferromagnetic resonance (FMR) frequency, allowing for the tuning of the EM wave absorption frequency range. W-type hexaferrite–epoxy composites (10 wt%) with x values between 0.6 and 1.5 exhibited outstanding wideband EM wave absorption, with a maximum absorption (RLmin < −50 dB) and a wide absorption bandwidth where RL < −10 dB extended beyond 10 GHz (Δfwb > 10 GHz). The x = 1.25 sample with a thickness of 2.37 mm achieved RLmin = −69 dB at 7.8 GHz, while the x = 1.0 sample with a thickness of 2.33 mm delivered Δfwb = 12.5 GHz (5.1–17.6 GHz). Samples synthesized via the molten-salt method showed larger plate-like grain growth compared to those produced by the solid-state method, with permeability spectra shifting to lower frequencies, consequently lowering the EM wave absorption band.

Magnetic chimeras in voltage-driven nano-oscillators

The emergence of spatiotemporal coherence is ubiquitous in nature. Intriguingly, in systems with uniform energy injection and dissipation mechanisms, coherent regions can be neighboring zones with non-coherent (e.g., chaotic or quasi-periodic) motions, giving rise to the so-called chimera states. This article studies the chimeric self-organization of magnetic nano-oscillators coupled with dipolar fields under energy losses and injection. The chimera states arises from an alternating voltage that, in the presence of insulating barriers, modulates the magnetic anisotropy fields, an effect known as voltage-controlled magnetic anisotropy. This field allows the efficient manipulation of the magnetization because it can produce magnetic switching and resonances, among other dynamic responses, while avoiding the Joule heating. In the classical limit, magnetization dynamics are governed by the Landau–Lifshitz equation. We consider three setups composed of N={4,6,10} interacting oscillators, each one of them regarded as a macrospin that moves rigidly. Our main results are Small magnetic chimeras, Weak magnetic chimeras, and a meta-chaos state. Chimera states are composed of a synchronized and a chaotic group of oscillators, both sets typically having hundreds of units; on the other hand, small chimeras are composed of a few – usually around five – oscillators dividing into coherent and non-coherent regions. A weak chimera has two or more sets of coherently oscillating units, but the groups possess different frequencies. Finally, the meta-chaos state is a chaotic transient. Beyond the previous zoology, fully synchronized states are also present, as the bifurcation diagram reveals.

Stability of Noncentrosymmetric Square Skyrmion Crystals with Easy-Axis and Easy-Plane Magnetic Anisotropy

We investigate the stability tendency of a magnetic skyrmion crystal in noncentrosymmetric tetragonal systems with the Dzyaloshinskii–Moriya interaction. We show that the stability region of the square skyrmion crystal on a square lattice depends on the Ising-type magnetic anisotropic interaction by performing the simulated annealing for the spin model. The easy-axis anisotropic interaction tends to narrow the region where the square skyrmion crystal is stabilized when the magnetic field is applied in the out-of-plane direction. In contrast, the easy-plane anisotropic interaction tends to enlarge the stability region. Meanwhile, the square skyrmion crystal induced by the easy-axis anisotropic interaction is robust compared with that induced by the easy-plane anisotropic interaction when the magnetic field is tilted from the out-of-plane to the in-plane direction. The results indicate that the instability toward the square skyrmion crystal in noncentrosymmetric crystals is sensitive to both magnetic anisotropy and magnetic fields.

Magnetic-field-controllable elasticity of helical spring magnets composed of magnetic-particle-polymer composites

Abstract We experimentally demonstrated the ability to control the spring constant of helical mechanical springs using a magnetic field. These springs were composed of magnetic nanoparticles embedded within an elastic polymer matrix. The composite material, in its gel form, was injected into a 3D-printed mold featuring a helical-spring-shaped cavity. An external magnetic field applied perpendicular to the coil axis of the spring allows the aligmment of the magnetic nanoparticle assemblies (chain axis) in the field direction. This alignment process determines the preferred magnetization orientation of the particle assembly chain, thereby balancing the magnetic force between the magnetic anisotropy field and the Zeeman field under a given external field. When the spring is subjected to compression or stretching loads under an externally applied magnetic field, these two magnetic fields modify the effective spring constant of the magnetic helical spring by ~ 31 %, incresing it from 8.7 N/m (under no field) to 11.5 N/m at 300 mT. Analytical modeling using a simplified rod geometry aptly explains the experimental results, demonstrating that the spring constant linearly increases with the field strength up to 300 mT. Such composite magnetic helical springs could be utilized as active vibration absorbers or isolators due to their field-controllable elasticity.

A two-step self consistent algorithm for extracting magnetic anisotropy constants from angle-dependent ferromagnetic resonance measurements

To infer anisotropy parameters of magnetic materials from experimental measurements of ferromagnetic resonance (FMR) (with data comprising resonant frequencies and corresponding resonant magnetic fields), a fitting procedure to the theoretical model is essential. The governing equation for this fitting process is the Smit–Beljers equation (SB equation), which links FMR frequencies to resonant magnetic field values and anisotropy parameters nonlinearly, and through the equilibrium magnetization angle values, which also depend on the same anisotropy parameters and magnetic field values. Obtaining an analytical expression for this equation is rarely possible. In this paper, we address the challenges posed by the Smit–Beljers equation and propose a two-step self-consistent algorithm to extract the relevant parameters efficiently.

Electromagnetic wave absorption properties of La-Ca-Co-Al substituted M-type Sr-hexaferrite-rubber sheets in 50–75 GHz range

This study reports on the electromagnetic (EM) wave absorption characteristics of M-type hexaferrite-rubber sheets, where Al was additionally substituted into high-performance permanent magnet compositions, Sr0.2La0.4Ca0.4Co0.25Fe9.75-xAlxO19-d (LCCA-SrM, x = 0, 0.2, 0.4). While non-substituted SrFe12O19 powder-rubber sheet had a ferromagnetic resonance frequency (fFMR) of 48.5 GHz, the LCCA-SrM (x = 0, 0.2, 0.4) rubber sheets showed increased fFMR values of 63.3, 66.2, and 68.5 GHz, respectively, with the increasing x values. The frequency of minimum reflection loss (fRLmin) also increased correspondingly with the change in fFMR. This significant increase in fFMR and fRLmin is attributed to the greatly enhanced magnetocrystalline anisotropy from the La-Ca-Co substitution in SrM and the incremental increase in magnetic anisotropy field (Hani) due to Al substitution. The absorption band (Δf) satisfying RL < −10 dB, was 45.0–53.4 GHz for SrM, and 52.9–75, 50–75, and 59–74.2 GHz for the x = 0, 0.2, and 0.4 samples, respectively. The x = 0.2 sheets demonstrated the widest absorption, covering 50–75 GHz. This study is highly promising as it is the first to demonstrate the feasibility of developing an EM wave absorber sheet for frequencies above 50 GHz using hexaferrite powder synthesized via the solid-state method, which offers scalability and cost-efficiency for mass production.

A singlet-triplet hole-spin qubit in MOS silicon

Holes in silicon quantum dots are promising for spin qubit applications due to the strong intrinsic spin-orbit coupling. The spin-orbit coupling produces complex hole-spin dynamics, providing opportunities to further optimise spin qubits. Here, we demonstrate a singlet-triplet qubit using hole states in a planar metal-oxide-semiconductor double quantum dot. We demonstrate rapid qubit control with singlet-triplet oscillations up to 400 MHz. The qubit exhibits promising coherence, with a maximum dephasing time of 600 ns, which is enhanced to 1.3 μs using refocusing techniques. We investigate the magnetic field anisotropy of the eigenstates, and determine a magnetic field orientation to improve the qubit initialisation fidelity. These results present a step forward for spin qubit technology, by implementing a high quality singlet-triplet hole-spin qubit in planar architecture suitable for scaling up to 2D arrays of coupled qubits.

Impact of Co2+ substitution on structure and magnetic properties of M-type strontium ferrite with different Fe/Sr ratios

Abstract Ion substitution has significantly improved the performance of ferrite magnets, and cobalt remains a key area of research. Studies on the mechanism of Co2+ in strontium ferrite, especially SrFe2n–x Co x O19–δ (n = 6.1–5.4; x = 0.05–0.20) synthesized using the ceramic method, showed that Co2+ preferentially enters the lattice as the Fe/Sr ratio decreases. This results in a decrease in the lattice constants a and c due to oxygen vacancies and iron ion deficiency. The impact of Co substitution on morphology is minor compared to the effect of the Fe/Sr ratio. As the Fe/Sr ratio decreases and the Co content increases, the saturation magnetization decreases. The magnetic anisotropy field exhibits a nonlinear change, generally increasing with higher Fe/Sr ratios and Co content. These changes in the performance of permanent magnets are attributed to the absence of Fe3+ ions at the 12k + 2a and 2b sites and the substitution of Co2+ at the 2b site. This suggests that by adjusting the Fe/Sr ratio and appropriate Co substitution, the magnetic anisotropy field of M-type strontium ferrite can be effectively optimized.

Microstructural and Magnetic Characteristics of Nanocrystalline Sm4ZrFe33 Alloys

This work focuses on the study of the microstructure and magnetic properties of nanocrystalline powders of Sm4ZrFe33, prepared by high‐energy ball milling. The Sm4ZrFe33 compound adopts a monoclinic structure (space group Cm). Upon annealing, these Sm4ZrFe33 samples exhibit notable variations in their extrinsic magnetic properties, closely linked to temperature fluctuations. The investigation delves into the correlation between morphology, grain size and magnetic characteristics. A significant enhancement in coercivity (Hc), remanent magnetization (Mr), and maximum energy product ((BH)max) is observed, primarily attributed to the finer grain structure present in the samples. Particularly noteworthy, among all annealed specimens, the nanocrystalline Sm4ZrFe33 compound annealed at a temperature of Ta = 973 K demonstrates the most promising magnetic properties. This specimen exhibits a coercivity Hc of 18 500 Oe, remanent magnetization (Mr) of 58 emu g−1, maximum energy product ((BH)max) of 5.18 MGOe, Curie temperature (TC) of ≈804 K, and magnetic anisotropy field (Ha) of 115 980 Oe. These research findings pave the way for future investigations and applications in the realm of permanent magnets, spintronic devices, and magnetic recording, utilizing nanocrystalline alloys based on the Sm4ZrFe33 compound.

Perpendicular magnetic anisotropy of Cr/CoFeB/MgO modulated by MgO thickness

The dependence of perpendicular magnetic anisotropy (PMA) on the MgO thickness in Cr/CoFeB/MgO/Ta films has been experimentally investigated. A clear PMA is observed in the as-deposited samples with 1.8 nm MgO while no as-deposited PMA is shown in those with 4.0 nm MgO. This may be attributed to the moderate oxidation degree of CoFeB and larger interfacial anisotropy energy density K i to overcome the volume magnetic anisotropy and demagnetization field. On the contrary, samples with 4.0 nm MgO demonstrate PMA only after annealing, which might be due to the oxygen and boron diffusion during the annealing process. These results would provide a method to optimize the design of CoFeB/MgO structures on 3d metals for future applications in perpendicular magnetic devices.

Magnetic anisotropy and GGG substrate stray field in YIG films down to millikelvin temperatures

Quantum magnonics investigates the quantum-mechanical properties of magnons, such as quantum coherence or entanglement for solid-state quantum information technologies at the nanoscale. The most promising material for quantum magnonics is the ferrimagnetic yttrium iron garnet (YIG), which hosts magnons with the longest lifetimes. YIG films of the highest quality are grown on a paramagnetic gadolinium gallium garnet (GGG) substrate. The literature has reported that ferromagnetic resonance (FMR) frequencies of YIG/GGG decrease at temperatures below 50 K despite the increase in YIG magnetization. We investigated a 97 nm-thick YIG film grown on 500 μm-thick GGG substrate through a series of experiments conducted at temperatures as low as 30 mK, and using both analytical and numerical methods. Our findings suggest that the primary factor contributing to the FMR frequency shift is the stray magnetic field created by the partially magnetized GGG substrate. This stray field is antiparallel to the applied external field and is highly inhomogeneous, reaching up to 40 mT in the center of the sample. At temperatures below 500 mK, the GGG field exhibits a saturation that cannot be described by the standard Brillouin function for a paramagnet. Including the calculated GGG field in the analysis of the FMR frequency versus temperature dependence allowed the determination of the cubic and uniaxial anisotropies. We find that the total crystallographic anisotropy increases more than three times with the decrease in temperature down to 2 K. Our findings enable accurate predictions of the YIG/GGG magnetic systems behavior at low and ultralow millikelvin temperatures, crucial for developing quantum magnonic devices.

Finite element modeling of the magnetic property behaviors of electrical steels in rotating fields considering their crystallographic textures

In magnetic device modeling, the crystallographic textures and microstructures of electrical steels critically influence their magnetic properties. Yet, these aspects are often neglected or inadequately represented in finite element (FE) models, leading to inaccuracies in predicting electrical steel performance, especially in complex electromagnetic environments. This paper presents a multi-scale modeling approach, integrating a macroscopic FE model of a magnetic device with a microstructural scalar permeability model that accounts for the crystallographic textures of electrical steels. This approach demonstrates proficiency in predicting nonlinear anisotropic permeability and capturing magnetic anisotropy of electrical steels within a rotational tester, especially when anisotropy is predominantly governed by crystallographic texture and the angles between the B and H vectors are minimal. Furthermore, the model effectively captures the magnetic anisotropy in complex magnetic fields and geometric configurations of a permanent magnet motor. A comparative analysis of this model is conducted against three other material models: an isotropic model, a two-axis model, and a general-vector model. These models are based on different approaches, ranging from a single non-linear BH curve to comprehensive vector BH curves covering all directions. Among them, the general-vector model, reliant on extensive 2D vector BH measurements, is the most accurate but requires substantial experimental data.

Electric field control of 180° magnetization reversal in a spin-valve multiferroic heterostructure

Electrical tuning of magnetism, rather than a spin current or magnetic field, has attracted much attention due to its great potential for designing energy-efficient spintronic devices. However, pure electric field (E-field) control of 180° magnetization reversal is still challenging. Thus, we report an E-field-controlled 180° magnetization reversal in a spin valve (SV)/Pb(Mg1/3Nb2/3)0.7Ti0.3O3 (PMN-PT) multiferroic heterostructure. Via the converse magnetoelectric coupling effect in CoFe/PMN-PT heterostructures, the magnetic anisotropy and coercive field of the CoFe film can be tremendously modulated by an E-field. We fabricated an optimized SV grown on the PMN-PT substrate, in which the magnetic moments of the free and pinned layers are parallel to each other at the initial state. By applying an E-field, the coercive field of the free layer was enhanced, exhibiting an antiparallel configuration between the free and pinned layers. Based on the theoretical and experimental results, a complete 180° magnetization reversal of the free layer can be obtained without a magnetic field. Accordingly, an E-field-controlled giant, reversible and repeatable magnetoresistance modulation can be achieved. This work proposes a feasible strategy to achieve E-field-controlled 180° magnetization reversal, which is critical for exploring ultralow power consumption magnetic memory devices.

Thermal Annealing Impact on the Sensitivity of Piezomagnetic Surface Acoustic Waveguide to Applied Magnetic Field

AbstractMagnetostrictive thin films, exhibit significant utility as functionalization materials for Surface acoustic wave sensors designed for magnetic field measurements. This research investigates the influence of annealing under vacuum and magnetic field at various temperatures on the magnetic properties of the FeCo/TbCo2 thin film and therefore on the sensitivity of shear and Rayleigh acoustic waveguides functionalized with these magnetic layers. The observed effects include a reduction in magnetic anisotropy field and an increase in magnetostriction. XPS and TEM coupled with EDS microanalysis provide insights into the variations in the properties of the nanostructured magnetic film. To safeguard the magnetic film, a thin layer of SiO2 is deposited on top, serving as a protective shield. The inclusion of this layer amplifies sensitivity to applied magnetic fields for modes with shear polarization while reducing sensitivity for Rayleigh mode. In ST‐cut Quartz, the shear waves become waveguided upon the incorporation of magnetic thin films, with further enhancement achieved by introducing a SiO2 layer. Rayleigh waves are evanescent modes, the penetration depth is in the order of wavelength, and the addition of SiO2 decrease the wave confinement and therefore the sensitivity. The findings are supported by a theoretical model and experimentally validated results.

A novel approach for measuring large magnetic anisotropy energy with a limited magnetic field range

Here we propose an experimental method for determining the magnetic anisotropy field in ferromagnetic materials. Our method involves examining the small-angle variation of spontaneous magnetization by the external magnetic field and interpreting the experimental result within the framework of the Stoner-Wohlfarth model applicable to ferromagnetic materials. This method allows for the extrapolation of magnetic anisotropy fields, even when they surpass conventional measurement limits. As a result, a broad range of magnetic anisotropy fields can be ascertained using a single experimental setup. Our proposed method serves as a versatile tool for analyzing large magnetic anisotropy energy which is an important parameter for future spintronic devices.

Excellent intrinsic magnetic properties in the TbCu7-type Sm-Fe-N compound

We report excellent intrinsic magnetic properties of SmFe9Nδ epitaxial thin films with TbCu7-type crystal structure, i.e., room temperature saturation magnetization (μ0Ms) of 1.64 T, Curie temperature (Tc) of 771 K and magnetic anisotropy field (μ0HA) of ∼22 T for δ=1.1, the saturation magnetization of which is superior to that of Sm2Fe17N3 (μ0Ms= 1.57 T) and Nd2Fe14B compounds (μ0Ms= 1.61 T). X-ray diffraction and transmission electron microscopy revealed that the thin films have a highly textured single TbCu7-type phase with its c-axis perpendicular to the film. Heat treatment of the thin films under N atmosphere expands the lattice and increases the unit cell volume of the SmFe9Nδ structure, which also switches the magnetocrystalline anisotropy from easy plane (δ = 0) to easy axis (δ=1.1). Furthermore, the μ0Ms and Tc of SmFe9Nδ films also increased with increasing nitrogen content in the structure, leading to promising intrinsic magnetic properties. Based on this study, we can conclude that the rare-earth lean SmFe9Nδ based TbCu7-type compound has potential for the development of high performance anisotropic bonded magnets with superior performance to that of existing anisotropic Sm2Fe17N3 or Nd-Fe-B bonded magnets.

Modulation of switching current density in T-type magnetic structure through magnetic anisotropy

We investigate magnetic field driven domain wall motion and spin-orbit torque (SOT) induced perpendicular magnetization switching of the ferrimagnetic layer in a T-type magnetic heterojunction with the structure of Pt/Co/Ta/Co81Tb19/Ta, where the bottom Co layer has in-plane magnetic anisotropy and the top Co81Tb19 layer has perpendicular magnetic anisotropy. It is found that the magnetic field driven domain wall motion and the depinning field of the Co81Tb19 layer can be effectively tuned by the thickness of the Co layer (tCo). Meanwhile, SOT-induced perpendicular magnetization switching of the Co81Tb19 layer is observed, and the critical switching current density first decreases and then increases with increasing the thickness of the Co layer. A lower critical switching current density was obtained at the optimized thickness (tCo = 1.2 nm), resulting in a 37% reduction in critical switching current density. Meanwhile, the research reveals a strong correlation between critical switching current density and magnetic anisotropy field, indicating that tuning the magnetic anisotropy is an efficient way to modulate the switching current density in a T-type magnetic structure. These results provide a new perspective on SOT manipulation and will be useful for the design of SOT-based devices.

Growth of thin-film magnetic nanostructures promising for spintronics applications

Multilayered metallic nanostructures are promising for the fabrication of spin valves based on the giant magnetoresistive effect and for studies of the nature of topological magnetism, aimed at the development of new nanoscale data storage and transfer devices, e.g. those based on magnetic skyrmions. It is still an important task to develop methods of synthesis and configuration of thin-film nanostructures and control of spin textures in those nanostructures under electric and spin currents generated as a result of the spin Hall effect in external electric fields. Thin-film polycrystalline ferromagnetic / heavy metal Ru(10nm)/Co(0,8)/Ru(2), Ru(10)/Co(0,8)/Ru(2)/W(4), Pt(5)/Co(0,8)/MgO(2)/Pt(2) and Pt(15)/Co(0,8)/MgO(2)/Pt(2) nanostructures have been synthesized using magnetron sputtering. Electric contacts and Hall structures with different conductive bridge thicknesses have been synthesized on the specimens using electron beam photolithography. Experimental vibration magnetometric data have been utilized to calculate magnetic parameters of the specimens, i.e., saturation magnetization, magnetic anisotropy energy and field and coercive force as functions of ferromagnetic and heavy metal layer types. The domain structure of the specimens has been studied using Kerr microscopy. The electrical resistivity has been simulated and the critical current and current density of the nanostructures have been assessed. We show that all the film specimens exhibit perpendicular magnetic anisotropy and can be used in the studies of current-induced phenomena and spin moment transfer processes in nanostructures.

Influences of divalent ion substitution on the magnetic and dielectric properties of W-type barium ferrite

Abstract Saturation magnetization, magneto-crystalline anisotropy field and dielectric properties are closely related to microwave devices applied at different frequencies. For regulating the magnetic and dielectric properties of W-type barium ferrites, single-phase BaMe 2Fe16O27 (Me = Fe, Mn, Zn, Ni, Co) with different Me ions were synthesized by the high-temperature solid-state method. The saturation magnetization (M s) range from 47.77 emu/g to 95.34 emu/g and the magnetic anisotropy field (H a) range from 10700.60 Oe to 13739.57 Oe, depending on the type of cation substitution in the hexagonal lattice. The dielectric permittivity and dielectric loss decrease with increasing frequency of the AC electric field in the low-frequency region, while they almost remain constant in the high-frequency region. The characteristics of easy regulation and preparation make it a potential candidate for use in microwave device applications.